Ionescu Ștefania, [606501]

Ionescu Ștefania,
Behavio ral Economics I

A brief history on the saving concept

Why do people save money instead of spending them? What were the theories that trie d to
explain the saving behavio r in the past years? This essay tries to answer this questions and
aims to broad the understanding of the saving concept over the time.
At the beginning of the 18th century, Halley created a formula for the present value, “ the
value of a good depends on the timing of its consumption” and he was among the firsts to
formalize the idea that the utility for the present goods is different for the future goods. In
1843, the Scottish economist, John Rae, says that saving is based on the effective wish for
accumu lation. This wish is based on four concepts : the bequest motive, the self -restrain, the
uncertainty of human life and the excitement of immediate consumption. The first two are
considered to promote the wish for expenditure and the last two are supposed t o decrease it.
But taking all four of them together will define a person’s time preference. For example, the
more uncertainty a consumer has over his life the less he will care about the future, and,
consequently, the lower will be his desire of accumulati on. In the same time, the higher his
affections towards his heir , the more value he will give to the future, and, consequently, the
higher is his willingness to save money .
Later on, in 1871, William Stanley Jevons presents a more technical view upon t he saving
behaviour. His theory says that in order to maximize total utility ( pleasure ) over time, an
individual should distribute consumption of a “x” days to equal each days the marginal
utilitay multiplied by the probability of the good remaining cons umable. In less technical
words, if I have 100 monetary units today, I should not spend them all now, I should divide
the utility in the number of days where i expect to buy goods and services that would bring be
the same amount of utility every day. . In 1890 Eugen von Böhm -Bawerk claims that there is
a systematic tendency to underestimate future needs because individuals do not have a
complete view of their future wants. This means that an individual doesn’t have the ability to
correctly predict his/her f uture wants and therefore, they will underestimate future needs and
will not take the decision to save money. In 1930, Irwin Fischer – reached “a formalization of
time preference in terms of economic trade -offs among consumption in two different periods;
every person has his own rate of ‘impatience’, and this rate is dependent upon objective

factors (size and risk of future income) and subjective factors (foresight, strength of will,
habit, uncertainty, selfishness, influence of fashion). But Fisher’s the ory aimed at describing
equilibrium in the financial market, where all different rates of impatience would have been
homogenized by the invisible hand , the the market interest rate (through borrowing and
lending).
The most famous theory, is Paul Samuels on’s, in 1937, the Discounted Utility Model with the
following mathematical equation that defines the saving behaviour:

where V(x, t) is the utility value of income x occurring in time distance t
His theory came with the following assumptions for the the ory : the consumer acts so as to
reach the maximum of all future utilities; Future utilities need to be «dimished to comparable
magnitudes by appropiate time discounting; discounting was considered independent
(separate) from utility and individuals dis count exponentially.
In 1956, Robert Strotz came with an explanation why people discount exponentially:
exponential discounting is the only discount function that guarantees the principle of dynamic
consistency. In other words, Strotz showed that if a cons umer’s time preferences had a
structure different from exponential discounting, then he would be unable to follow his own
plans. Let’s assume that an individual would choose €110 in 3 days over €100 in 2 days, but
chooses €100 now over €110 tomorrow. Fro m the distance, he wantss the larger -later
amount, but once he approaches consumption, he cannot remain to his previous decision and
decides to go for the smaller -immediate amount. Such a consumer would have a certain
behaviour planned, but continuously r econsider his decision without ever being able to stick
to previous plans.The effect, as Strotz proved in a more general setting, is that, in order to
rule out dynamic inconsistency from the individual’s behavior, we need to suppose
exponential discounting , or, as it is often labeled, constant discounting. Constant discounting
means that in every period the same discount rate (or factor) is applied, and thus the same
proportion of value is discounted. Several papers have been published to provide an in -depth
description about the assumptions of the discounted utility model such as Koopmans (1960),
Lancaster (1963) and Albrecht & Weber( 1995) .
Later on, other researchers questioned the basic assumptions of the discounted utility model.

In 1981, Thaler began testing the hypothesis of the declining discount rate.His studies prove
the hyperbolic discounting hypothesis. In short words, this theory says that instead of
remaining constant over time, discounting rates decline over the time, people think about
postponing consumption one period a bigger sacrifice when the period is close than when it is
far in the future.
Hyperbolic discounting has been further developed in 1997 by Laibson. His research
basically proposes a more general hyperbolic discounting theory to explain the saving
behaviour.
On the other hand, the anomalies of the hyperbolic discounting model have been researched
starting from 1975 with Yates & Watts whose study prove that people prefer to delay losses.
In 1987, Loewenstein justifies the viola tions of the axioms of the model are explained by the
constructs of anticipal pleasure and pain. After this, Benzion et al. had a study in 1989 whose
results rejected the hypothesis that the discount rate is uniform across different time and sum
scenarios reveal the “sign effect”; winning or accumulating is discounted at a higher rate than
losing. Similar results have been found out also in other areas such as health, published in
1993 by Mackeigan et al. The magnitude effect explains that an increased amou nt is
discounted at a lower rate and in the same time a decreased amount of money is discounted at
a higher rate and this strongly impacts the intertemporal choice. Also, a successiveness of
gains will be discounted at a lower rate than single gains. This means that an individual will
be less likely to make savings in case he receives a sequence of incomes rathen than receiving
an individual one (Thaler 1981)
Behavioural economics research reveals that the amount, source, and nature of the
information indi viduals receive about saving are likely to influence savings decisions.
Thaler and Shefrin (1981) describe this internal struggle as a conflict between a “farsighted
planner” and a “myopic doer.”
In conclusion, There is significant number of anomalies that disapprove discounted utility
model as a descriptive theory of intertemporal choice. The studies are quite intuitive and most
of us could be represented by these models, by these patterns, even though they cannot be
linked to Samuelson’s mathematical structure. It is interesting that the discounted utility is
still regarded as the standard approach taught in most Economy schools. An alternative model
has not been yet established and widely accepted and the research directions are still broad
for furthe r discoveries.

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